1. Field of the Invention
The invention relates to an active control system for protecting a structure, such as a building, from disturbances, such as vibrational disturbances, by imparting canceling forces to the structure. More particularly, it relates to a plural orthogonal controlling force apparatus, having a corresponding number of plural time domain digital controllers, with input and output sensor arrays which work on orthogonal components of the disturbance. The apparatus is capable of attenuating simultaneously signals with spectra consisting of multiple narrowband character, or combined narrowband and broadband character. The invention has particular applicability to controlling or counteracting seismic or other environmentally induced disturbances.
2. Description of Related Art
Vibration control systems for attenuating undesirable wind, earthquake and mechanical vibrations are known. Many of these prior vibration control systems are passive systems such as the base isolation and the dynamic absorber type control systems that are commonly used to attenuate unwanted vibrations. Patents relating to various techniques for wind and earthquake disturbance control include U.S. Pat. Nos. 4,783,937; 4,799,339; 4,841,685; 4,429,496; 4,635,892; 4,922,667; 4,956,947; 4,766,706; 5,025,599; 5,036,633; 5,107,634; 5,233,797; 5,239,789; 5,245,807; 5,255,764; and 5,311,709. However, because the character of the undesired vibrations may change over time, active vibration control may provide better attenuation abilities than passive systems. A combination of active and passive methods may provide the best protection against unwanted vibrations, particularly from earthquakes.
A known prior art controller for wind and earthquake disturbances by Nishimura (Nishimura, Isao et al., "An Experimental Study of the Active Control of a Building Model," Proceedings of the First Joint U.S./Japan Conference on Adaptive Structures, Maui, Hawaii, Nov. 13-15, 1990) is depicted in FIG. 1. It is based on feedback analysis. This system does not have an upstream sensor array to measure the disturbance signal, x.sub.k, before the disturbance enters the structure; all responses are measured by the downstream sensors to give the output or error e.sub.k. The error signal e.sub.k is fed into an analysis box to give the cancellation signal u.sub.k which is imparted to the system by an actuator. It is a closed loop controller. The control law is a linear feedback control system based on the first order differential equation model of the system. This control system requires development of a good model for the building or structure before the controller is installed. State space based controllers have difficulty with time lags. If the time lag, between the time the disturbance is sensed and the time the correcting force is applied, is too long this type of controller does not work well.
A prior art controller for earthquake disturbances by Kobori et. al. (U.S. Pat. No. 4,799,339) is shown in FIG. 2. This controller is a feed forward frequency domain controller 10" based on a single frequency with upstream sensors 4" near the building and close to the source of the seismic disturbance. (In addition to the feed forward controller, a feedback controller to modify the rigidity of the building by stiffness connectors 5 is also incorporated.) The downstream sensors 6" are on the building 2". Though this is a feed forward controller it is significantly different than the present invention since it is not only frequency domain based but also limited to a single frequency. This system has two upstream sensor sites 4"; one at the epicenter 4"A of the earthquake and the second consisting of two sensors in the ground near the building 4"B. This assumes that the network of seismic monitoring sites is extensive so that any earthquake epicenter will be monitored by a nearby sensor. This may be feasible in Japan or California but may be difficult elsewhere. The schematic shows the sensors 6" within the building 2" and the controller 10". In addition, this system strives to change the rigidity to reduce the vibration of the building as well as control the excess disturbance. The addition of the rigidity modifications 5" then changes the transfer functions of the controller with time making this a very difficult control problem. The patent description of this prior art does not discuss the details of the controller other than to say that it "analyzes frequency characteristics and calculatively forecasts the oscillatory property" (U.S. Pat. No. 4,799,339, column 5, lines 57-58).
Other control systems of the digital feed forward type are also known in the art. Much of the early work in digital feed forward control systems occurred in the acoustic field arena for noise attenuation in a fan duct using a speaker to introduce the canceling sound wave. Prior control systems for acoustic systems use adaptive filtering based on the Least Mean Square (LMS) algorithm in various configurations to estimate the required cancellation signal to be introduced into the system. Examples of these techniques include U.S. Pat. Nos. 5,337,365; 5,325,437; 5,355,417; 5,377,275; and 5,377,276. Prior control systems based on the LMS will adapt successfully for strictly broadband or narrowband characteristic input signals but, if the input signal spectrum consists of a broadband signal and a narrowband signal or of multiple close tones, the filter output may not converge, or, at best, converge extremely slowly. This is true because, when the condition number of the input correlation matrix is large, the LMS will not converge. Since many mechanical systems have multi-tonal input signals, this type of controller is not generally applicable.
Input signals with both broadband and narrowband characteristics in the frequency domain will be referred to as combined input. An example of combined input consists of colored noise (broadband) and multiple tonals (narrowband). Thus, prior control systems with the adaptive LMS filter may be used effectively and efficiently only in systems with input signals that have a strictly broadband or narrowband spectrum where the tones are well separated. In addition, prior control systems also have difficulty converging for narrowband signals consisting of multiple tones. A significant drawback of control systems with the LMS as the adaptive filter is their inability to converge rapidly (within k*n filter lengths, k&lt;10) for combined input. The convergence time may be such that the necessary action by the compensator or actuator to cancel the noise or vibration is applied too late and thus, instead of reducing the vibration, the problem becomes exacerbated.
FIG. 3 shows a known prior art filtered-X controller system developed by Burgess (Burgess, J. C., "Active adaptive sound control in a duct: A computer simulation," J. Acoust. Soc. Am., 70(3), Sep. 1981, pp. 715-726). This controller is designed for use with a Finite Impulse Response (FIR) filter adapted in the time domain using the LMS algorithm. This controller includes upstream 4' and downstream 6' sensors feeding into the controller 10'. The disturbance is sensed at the upstream sensor array 4' and then enters the object 2' generating the unwanted response. The canceling signal is added 8' and then the resulting output or error signal is sensed by the downstream sensor array 6'. P.sub.1 represents the transfer function between the upstream 4' and downstream 6' sensors. P.sub.2 represents the transfer function between the canceling force device and the downstream sensors. P.sub.2 represents an estimate of P.sub.2. The output error signal e.sub.k is fed into the LMS controller algorithm 20'B along with v.sub.k (the disturbance signal x.sub.k filtered by the estimate of P.sub.2 gives v.sub.k). The LMS algorithm determines the weights or coefficients which give the best canceling signal. These weights are then used to filter 20'A the disturbance signal to give q.sub.k. The signal, q.sub.k, is then applied to the object through the actuator array which is represented by P.sub.2 16' to give the cancellation signal y.sub.k. This controller does not have an anti-feedback filter so it has difficulty with non-ideal systems where there is contamination of the upstream sensor by the canceling signal. This controller works well for an ideal system if the input signal's spectrum consists of a single tone or of strictly white noise of broadband character. Because this control configuration is based on the LMS algorithm, as discussed above, it does not perform well for the combined problem or for the multiple tone problem.
Many practical systems experience the combined input such as tones in colored noise. This is frequently true in structural control. A stable control system which will handle combined input is necessary for structural vibration attenuation. Prior stable FIR systems adapt too slowly to actively control the physical system to reduce the vibrations of the system when the input consists of combined narrowband (tonals) and broadband spectrum signals. Thus, there is a need for a stable control system that can adapt rapidly for all types of input but, in particular, for the combined broadband/narrowband problem or the multiple tonal case.
In active adaptive filters such as those of Burgess discussed above and depicted in FIG. 3, to control unwanted signals there must be a canceling signal that is summed with the input signal to attenuate the input signal as it traverses the object to be controlled. The input and output signals must be measured by appropriately located sensors and the canceling signal must be generated by actuators and propagated into the structure. The structure to be controlled, and the sensors and actuators constitute the physical system. The physical system can be thought of as a number of "plants" interacting to produce the output. A "plant" is defined to be the transfer function between two nodes such as between the input and output sensor arrays, such terminology being well known in the art. The digital controller or electrical system consists of estimates of plant models, other filters and the adaptive algorithm that determines the cancellation signal.
The general goal of such control systems is to control the motion of the structure by minimizing the error signal. The canceling signal device is adapted by the system controller which may consist of various plant model estimates, a system model, and an adaptive algorithm in a specific controller configuration.
The present invention is based on the well-known concept of Finite Impulse Response (FIR) filters in the time domain. As such, only time domain FIR based methods will be discussed in detail. A FIR filter model, as is known, consists of a set of N+1 weights which represent a plant such that when convolved with the input data, produce an estimate to the actual plant output. A FIR filter is also referred to as an all zero filter because it requires only data entering the plant, x, and not output data, y. If we let b.sup.k .tbd.{b.sub.0.sup.k . . . b.sub.N.sup.k } be the set of N+1 filter weights at time k, and let x.sub.k be the input value at time k, and y.sub.k be the output value at time k, then the output at time k may be written as a linear combination of the filter weights with the past input values: EQU y.sub.k =b.sub.0.sup.k x.sub.k +b.sub.1.sup.k x.sub.k-1 +. . . +b.sub.N.sup.k x.sub.k-N.
The vector b may be fixed for all time or it may be adapted in time by an adaptive filter algorithm. In the z-domain the transfer function may be written as ##EQU1## It has a denominator of 1 indicating that no output values are required. It is called a finite impulse response filter (FIR) because when an impulse is applied to this system its response dies out in finite time. For a detailed explanation of the Z-domain and FIR filters, see Widrow & Stearns, Adaptive Filter Processing, Prentice Hall, 1985, Chapters 7 and 9 of this well-known text. Many times, in order to obtain a good approximation to the plant, N must be large. The value of N must be weighed in conjunction with the convergence rate of adaptive filter so that convergence is rapid enough for the system to be realizable.
The controller cannot control without a method to adjust the weights, b, which determine the canceling signal to be propagated into the system. The method of adjustment, the adaptive filter algorithm, is an integral part of any controller without which there can be no active control. The adaptive filter algorithm adjusts the weights at each time step based on some defined error criteria. The weights are adapted in time and will change at every time step until the adaptive filter algorithm has converged. If at a later time the input varies in time the weights will be adapted anew to match the new input characteristics. Adaptive algorithms that have been used in adaptive feed forward controllers include the Least Mean Square (LMS) and the LMS in normalized form (NLMS).
The LMS is a gradient descent method developed by Widrow (see Widrow & Stearns, Chapter 6). It uses a single past sample when adjusting the weights for the cancellation based on the error signal at the output sensor. It also has a scaling or acceleration parameter .mu. (also called the adaptive gain constant) that is determined by the user based on the problem of interest as is well known in the art (see, Widrow and Stearns, p. 111, Eq. 6.36). The LMS computes the weight update as: EQU e.sub.k =y.sub.k -y.sub.k EQU w.sub.k+1 =w.sub.k +2.mu.e.sub.k v.sub.k
where the above variables and coefficients are as shown in FIG. 3. It requires O(N) computations per sample and performs well for problems where the input data correlation matrix, R, has a small condition number (R=E[X.sup.T X] where X is the input data vector). [O(N) is read as Order(N) and means that the number of operations required per time step is proportional to N. This can be written as K*N, where K is a constant.]
The NLMS algorithm, as is well known, is the LMS normalized by .parallel.v.sub.k .parallel..sup.2. It computes the weight update as ##EQU2##
The Block Underdetermined Covariance (BUC) algorithm was developed by Slock (Slock, D. T. M., "The Block Underdetermined Covariance (BUC) Fast Transversal Filter (FTF) Algorithm for Adaptive Filtering," Proceedings of the 26th Asilomar Conference on Signals, Systems and Computers, 1992, incorporated by reference herein). The BUC is a modified block least squares method which uses an L.times.L estimate to the N.times.N input correlation matrix and a sliding window. It requires O(L.sup.2) computations, where L may be relatively small compared to N. It also has a scaling parameter that is set by the user. Unlike the LMS, the BUC is relatively insensitive to the condition number of the input correlation matrix.
The objective of the BUC algorithm, which governs the operation of the transversal filter, is to obtain the filter weights in such a way as to minimize the error, e, and find the weighted sum of the input signals that best fits the desired response. This objective is similar to that of the LMS. However, the methods by which the two algorithms determine the filter coefficients and minimize the error differ markedly. In the LMS, changes in the weight vector to accomplish this end are made along the direction of the estimated gradient vector based on the method of steepest descent on the quadratic error surface. The LMS relies on a single past sample value to determine the estimate of the filter weights. The BUC uses multiple past sample values (equal to a small percentage of the number of weights) to determine the estimate of the filter weights by minimizing the least squares criterion.
The BUC algorithm uses a window length L that is shorter than the FIR filter order N, leading to an underdetermined least squares problem to be solved. The BUC can treat successive blocks of data with no overlap or it can slide along the data advancing the block by as little as a single sample. A projection mechanism onto a subspace of dimension L renders the BUC's convergence less sensitive to the coloring of the input signal spectrum than is the case for the LMS algorithm. The underdetermined least squares character of the BUC also endows it with relatively fast tracking ability. In addition, the tracking ability of least squares type algorithms (such as the BUC) is independent of the condition number of the input correlation matrix.
The goal in selecting an adaptive filter algorithm for adjusting the filter weights is to enable fast convergence, without too many computational steps, and to produce the correct cancellation signal. When used as part of a feed forward controller, the LMS or NLMS algorithms converge quickly and accurately so long as the input signal is not a combined broadband and narrowband signal or is not a multiple tonal signal. With these latter inputs, the LMS/NLMS algorithm converges slower than the BUC, if it converges.
The BUC algorithm has not, to the applicant's knowledge, been used as an adaptive filter algorithm in a controller system. The BUC is expected to be slower than the LMS algorithm since it generally requires more computations per time step.